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ABSTRACT:
In this paper our goal is to explain the distribution of the sample coefficient of determination in the simple regression case. We do this by using its rela- tionship to the noncentral F distribution. But first we introduce a new term, the true coefficient of determination. In a simulation study it is feasible to know the true coefficient of determination because the variance of the error term is known. The usefulness of the true coefficient of determination is in the built of relationships with predetermined strength. It answers the question: How much error should we add? The answer depends on how strong we want the association in the simple regression model to be. Once we determine this we can compute the noncentrality parameter and explain the distribution of the sample coefficient of determination. It is a simple way of explaining the distribution of the sample coefficient of determination and it is interesting at least from the educational point of view.

SUGGESTED CITATION:
Nicolas Christou, "The True R² and the Truth about R²" (January 1, 2005). Center for the Teaching of Statistics. Paper 2005010101.
http://repositories.cdlib.org/uclastat/cts/2005010101